Parallel & Perpendicular Lines Parallel Lines:
Notes # Alpha 6
Two nonvertical lines are parallel iff their slopes are equal. Any two vertical lines are always parallel.
Standard Form of a Linear Equation: The standard form of a linear equation is +Ax + By = C, where A, B, and C are integers and A and B are both not zero. Ex A: Write the standard form of the equation of the line that is parallel to the given line and passes through the given point.
#1)
y = -4x – 7; (1, 5)
∕∕ Standard Form:
#2)
x – 5y = 4; (1, 4)
Note: Find the slope of the line. Then use that slope and the given point to write an equation in point-slope form. Then change the equation till it is in Standard Form.
∕∕ Standard Form:
Perpendicular Lines: Two nonvertical lines are perpendicular iff their slopes are negative reciprocals. Ex B: Write the standard form of the equation of the line that is perpendicular to the given line and passes through the given point.
#1)
y = 6x – 5; (0, 5)
Note: Find the slope of the line. Then use the negative reciprocal of the slope and the given point to write an equation in pointslope form. Then change the equation till it is in Standard Form.
⊥ Standard Form: Linear Relations & Functions Page 1 of 2
Parallel & Perpendicular Lines #2)
5x – y = 6; (1, -4)
⊥ Standard Form:
Ex C: Complete the following word problems. #1)
For what values of k is the graph of 2x – ky + 5 = 0 parallel to the graph of 3x + 7y + 15 = 0? For what value of k are the graphs perpendicular?
#2)
Show that quadrilateral PQRS is a rhombus if its vertices are P(3, 1), Q(8, 1), R(12, 4), and S (7, 4). Note: Find the slope of each equation. For parallel slope, set them equal to each other. Solve for k. For perpendicular slope, use the negative reciprocal of one of the slopes, set them equal to each other, and solve for k.
Linear Relations & Functions Page 2 of 2